Lebesgue Measure Preserving Thompson's Monoid
Abstract
This paper defines Lebesgue measure preserving Thompson's monoid, denoted by $\mathbb{G}$, which is modeled on Thompson's group $\mathbb{F}$ except that the elements of $\mathbb{G}$ are noninvertible. Moreover, it is required that the elements of $\mathbb{G}$ preserve Lebesgue measure. Monoid $\mathbb{G}$ exhibits very different properties from Thompson's group $\mathbb{F}$. The paper studies a number of algebraic (grouptheoretic) and dynamical properties of $\mathbb{G}$ including approximation, mixing, periodicity, entropy, decomposition, generators, and topological conjugacy.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 arXiv:
 arXiv:2010.00167
 Bibcode:
 2020arXiv201000167L
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 50 pages, 29 figures